Does any expert in the field know whether it is really the case that this intelligence we are seeing with frontier models is an "emerging" phenomena, only coming up when the architecture is scaled? Like isn't it weird that the 1 million parameter model with the same architecture can't solve basic puzzles but suddenly the 1 trillion parameter can conjure up counter-examples for the Jacobian conjecture? It's unintuitiv…
It's kind of sad that popular CS textbooks often focus on solving precise problems with lowest theoretical complexity bounds while ignoring more practical (but generally applicable) computation techniques.
In machine learning they call it "gradient descent", which in older days had analogies in techniques called "hill climbing", "local search" and "simulated annealing". Basically you have a function you need to optimize for, and you clumsily tweak the parameters so that you get the (locally) max/min value you wanted. These techniques were great at finding approximate, locally maximal solutions without trying all the possibilities at once (which is more akin to the kind of "brute force" in the traditional CS context).
I guess because these techniques were generally applicable yet the outputs were approximate and you couldn't analyze them much (no fancy O(n log n)), the theorists did not find them interesting and thus were not put into the spotlight of student's learning curricula.
In modern machine learning they do this gradient descent thing which is also tweaking the parameters bit by bit to optimize for the loss function, except that the parameters are now in the billions and trillions. The compute required is huge of course, but it's actually quite an "efficient" process, and it's not actually doing much of "brute forcing" at all. During training, the process is essentially, almost equivalent to, compressing the many many trillions of tokens of training data. To me it's quite amazing that they manage to complete such a process within a couple months of training, even if they have hundreds of thousands of GPUs...